I've found a four-digit number ABCD
such that

** ABCD=(A+B+C+D)**^{3}
What is it ?

Is it unique?

1) the cube root of 9999 is about 21.5, so A + B + C + D <= 21

2) Mod 9, ABCD = A + B + C + D. Cubing values mod 9, we see that the residues must be 0, 1 or -1.

3) Therefore, A+B+C+D must be in 0,1,8,9,10,17,18, 19

4) Cubing each of these values, we see that two or five work.

0^3 = 0000

1^3 = 0001

8^3 = 0512

17^3 = 4913

18^3 = 5832

5) So, no, Ady's value is not unique

*Edited on ***June 16, 2017, 10:18 am**